Motivated by recent experiments on light-matter interacting systems, we investigate a dilute Bose gas and self-bound quantum droplets in a one-dimensional optical lattice coupled to a lossy cavity mode. Using a classical-field approach, we determine the stationary states and collective excitations of this non-equilibrium system. Apart from the usual Bogoliubov modes, we identify a polariton-like gapped excitation, the frequency of which softens as a precursor of the density ordering transition. Moreover, its relaxation time diverges as the critical point is approached, signaling the non-equilibrium nature of this transition. Dynamically, this polariton-like mode can be probed by inducing cavity field fluctuations, which in turn generates spatio-temporal oscillations of both the condensate and droplet states. In the droplet regime, we also analyze the bound modes which bear the characteristics of such non-equilibrium self-bound state. In addition, we uncover solitonic non-equilibrium states, including condensate with kink-like configuration and double-droplet state, and investigate their robustness following a sudden quench. Remarkably, although these states become unstable beyond a critical coupling, they continue to manifest in the dynamics, akin to the scarring phenomena. Our results demonstrate that dissipative cavity coupling provides a versatile route for exploring rich non-equilibrium dynamics of condensates and quantum droplets within experimentally accessible settings.
Motivated by recent experiments on light-matter interacting systems, we investigate a dilute Bose gas and self-bound quantum droplets in a one-dimensional optical lattice coupled to a lossy cavity mode. Using a classical-field approach, we determine the stationary states and collective excitations of this non-equilibrium system. Apart from the usual Bogoliubov modes, we identify a polariton-like gapped excitation, the frequency of which softens as a precursor of the density ordering transition. Moreover, its relaxation time diverges as the critical point is approached, signaling the non-equilibrium nature of this transition. Dynamically, this polariton-like mode can be probed by inducing cavity field fluctuations, which in turn generates spatio-temporal oscillations of both the condensate and droplet states. In the droplet regime, we also analyze the bound modes which bear the characteristics of such non-equilibrium self-bound state. In addition, we uncover solitonic non-equilibrium states, including condensate with kink-like configuration and double-droplet state, and investigate their robustness following a sudden quench. Remarkably, although these states become unstable beyond a critical coupling, they continue to manifest in the dynamics, akin to the scarring phenomena. Our results demonstrate that dissipative cavity coupling provides a versatile route for exploring rich non-equilibrium dynamics of condensates and quantum droplets within experimentally accessible settings.
The self-organization of a Bose-Einstein condensate (BEC) in a transversely pumped optical cavity is a process akin to crystallization: when pumped by a laser of sufficient intensity, the coupled matter and light fields evolve, spontaneously, into a spatially modulated pattern, or crystal, whose lattice structure is dictated by the geometry of the cavity. In cavities having multiple degenerate modes, the quasicontinuum of possible lattice arrangements, and the continuous symmetry breaking associated with the adoption of a particular lattice arrangement, give rise to phenomena such as phonons, defects, and frustration, which have hitherto been unexplored in ultracold atomic settings involving neutral atoms. The present work develops a nonequilibrium field-theoretic approach to explore the self-organization of a BEC in a pumped, lossy optical cavity. We find that the transition is well described, in the regime of primary interest, by an effective equilibrium theory. At nonzero temperatures, the self-organization occurs via a fluctuation-driven first-order phase transition of the Brazovskii class; this transition persists to zero temperature and crosses over into a quantum phase transition. We make further use of our field-theoretic description to investigate the role of nonequilibrium fluctuations in the self-organization transition, as well as to explore the nucleation of ordered-phase droplets, the nature and energetics of topological defects, supersolidity in the ordered phase, and the possibility of frustration controlled by the cavity geometry. In addition, we discuss the range of experimental parameters for which we expect the phenomena described here to be observable, along with possible schemes for detecting ordering and fluctuations via either atomic correlations or the correlations of the light emitted from the cavity.
Excitons-polaritons of semiconductor microcavities are quasiparticles originating from the dressing of optical cavity photons by the interactions between quantum well electron-hole pairs. In planar geometry, their belonging to the family of quantum fluids has been many times demonstrated through the observation of macroscopic coherence phenomena, such as superfluidity and Bose-Einstein condensation. Like ultracold atoms, polaritons support on their surface a set of collective excitations, the Bogoliubov modes, whose spectrum encompasses the key information to describe the dynamics of quantum fluids. In this thesis, we present a wide variety of results concerning the detection and control of such modes in different configurations. Thanks to the development of a new high-resolution coherent spectroscopy method, we carried out a detailed study of the spectrum of polariton collective excitations. In particular, we highlighted the effects of the driven-dissipative nature of the system on the fundamental dynamics of the fluid, by investigating the interplay between the Bogoliubov modes and the polariton bistability under coherent pumping. This was the opportunity to reveal, in addition to the well-known phonon-type excitations, precursors of dynamical instability and the so-called ghost branch. Moreover, we studied the behavior of out-of-equilibrium phase transitions: first, via the effect of the system dimension on the bistability and, second, with the onset of a Goldstone mode, as a result of a spontaneous symmetry breaking in a parametric oscillation regime. Finally, we designed a pumping geometry that directly controls the instability modes between dark solitons of a pair guided by an intensity channel, leading to the formation of vortex-antivortex streets in the density.
The self-organization of a Bose-Einstein condensate (BEC) in a transversely pumped optical cavity is a process akin to crystallization: when pumped by a laser of sufficient intensity, the coupled matter and light fields evolve, spontaneously, into a spatially modulated pattern, or crystal, whose lattice structure is dictated by the geometry of the cavity.In cavities having multiple degenerate modes, the quasicontinuum of possible lattice arrangements, and the continuous symmetry breaking associated with the adoption of a particular lattice arrangement, give rise to phenomena such as phonons, defects, and frustration, which have hitherto been unexplored in ultracold atomic settings involving neutral atoms.The present work develops a nonequilibrium field-theoretic approach to explore the self-organization of a BEC in a pumped, lossy optical cavity.We find that the transition is well described, in the regime of primary interest, by an effective equilibrium theory.At nonzero temperatures, the self-organization occurs via a fluctuation-driven first-order phase transition of the Brazovskii class; this transition persists to zero temperature and crosses over into a quantum phase transition.We make further use of our field-theoretic description to investigate the role of nonequilibrium fluctuations in the self-organization transition, as well as to explore the nucleation of ordered-phase droplets, the nature and energetics of topological defects, supersolidity in the ordered phase, and the possibility of frustration controlled by the cavity geometry.In addition, we discuss the range of experimental parameters for which we expect the phenomena described here to be observable, along with possible schemes for detecting ordering and fluctuations via either atomic correlations or the correlations of the light emitted from the cavity.
We investigate the near-critical dynamics of atomic density fluctuations in the nonequilibrium self-organization transition of an optically driven quantum gas coupled to a single mode of a cavity. In this system cavity-mediated long-range interactions between atoms, tunable by the drive strength, lead to softening of an excitation mode recently observed in experiments. This phenomenon has previously been studied within a two-mode approximation for the collective motional degrees of freedom of the atomic condensate, which results in an effective open-system Dicke model. Here, including the full spectrum of atomic modes we find a finite lifetime for a rotonlike mode in the Bogoliubov excitation spectrum that is strongly pump dependent. The corresponding decay rate and critical exponents for the phase transition are calculated explaining the nonmonotonic pump-dependent atomic damping rate observed in recent experiments. We compute the near-critical behavior of the intracavity field fluctuations that has been previously shown to be enhanced with respect to the equilibrium Dicke model in a two-mode approximation. We highlight the role of the finite size of the system in the suppression of it below the expectations of the open Dicke model.
Optical lattice plays an important role on stability and dynamics of quantum droplets. In this letter, we investigate the Bogoliubov excitation spectrum of quantum droplets in optical lattice in the thermodynamic limit. We classify the collective excitations as synchronous modes, Bloch phononic modes, and site-density imbalanced modes. For synchronous modes, we measure the dipole oscillation frequencies by quench dynamics with a sudden shift of the optical lattice, and the breathing frequencies by Floquet dynamics with a periodic change of the lattice depth. Bloch phononic modes are observable from the Landau critical velocity of the droplets. We further discuss the instability induced by the site-dependent density fluctuations, and calculate the critical filling of atoms where the growth of lattice vacancy breaks down the translational symmetry of the system. This work makes essential steps towards measuring the excitation spectrum and understanding the superfluid nature of quantum droplets in optical lattice.
The optical lattice plays an important role in the stability and dynamics of quantum droplets. In this article, we investigate the Bogoliubov excitation spectrum of quantum droplets in an optical lattice in the thermodynamic limit. We classify the collective excitations as synchronous modes, Bloch phononic modes, and site-population-imbalanced modes. For synchronous modes, we measure the dipole oscillation frequencies by quench dynamics with a sudden shift of the optical lattice and the breathing frequencies by Floquet dynamics with a periodic change of the lattice depth. Bloch phononic modes are observable from the Landau critical velocity of the droplets. We further discuss the instability induced by site-dependent density fluctuations and calculate the critical filling of atoms where the growth of lattice vacancy breaks down the translational symmetry of the system. This work makes essential steps towards measuring the excitation spectrum and understanding the superfluid nature of quantum droplets in an optical lattice.